Open AccessA EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIX
Author(s) -
I. Kalisperakis,
G. Karras,
E. Petsa
Publication year - 2016
Publication title -
isprs annals of the photogrammetry, remote sensing and spatial information sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.356
H-Index - 38
eISSN - 2194-9042
pISSN - 2196-6346
DOI - 10.5194/isprsannals-iii-3-75-2016
Subject(s) - epipolar geometry , fundamental matrix (linear differential equation) , essential matrix , translation (biology) , computer vision , coplanarity , orientation (vector space) , mathematics , artificial intelligence , position (finance) , rotation (mathematics) , rotation matrix , geometry , computer science , mathematical analysis , image (mathematics) , physics , symmetric matrix , biochemistry , eigenvalues and eigenvectors , chemistry , state transition matrix , finance , quantum mechanics , messenger rna , economics , gene
Epipolar geometry of a stereopair can be expressed either in 3D, as the relative orientation (i.e. translation and rotation) of two bundles of optical rays in case of calibrated cameras or, in case of unclalibrated cameras, in 2D as the position of the epipoles on the image planes and a projective transformation that maps points in one image to corresponding epipolar lines on the other. The typical coplanarity equation describes the first case; the Fundamental matrix describes the second. It has also been proven in the Computer Vision literature that 2D epipolar geometry imposes two independent constraints on the parameters of camera interior orientation. In this contribution these constraints are expressed directly in 3D Euclidean space by imposing the equality of the dihedral angle of epipolar planes defined by the optical axes of the two cameras or by suitably chosen corresponding epipolar lines. By means of these constraints, new closed form algorithms are proposed for the estimation of a variable or common camera constant value given the fundamental matrix and the principal point position of a stereopair.